Measuring the Hubble Constant through Cepheid Distances Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant Freedman, Madore, Gibson, et al., Astrophysical Journal 553, pp. 47. Brian Gleim AST 591 - Rolf Jansen
Introduction In standard Big Bang cosmology, universe expands uniformly according to: v = H 0 d, Hubble law Finding accurate value of H 0 is challenging primary difficulty is establishing accurate distances at cosmological scales
Uses of Hubble Constant H 0-1 sets the age of Universe: t 0 Size of observable Universe: R obs =c t 0 H 0 2 relates total energy density to geometry Critical density of Universe: crit =3H 2 /8G Many physical properties of galaxies and quasars, and abundances of primordial light elements all require knowledge of H 0
H 0 Key Project Goal: to measure H 0 based on Cepheid calibration of independent, secondary distance methods Avoids relying on a single method
H 0 Key Project Uses HST Cepheid distances to provide an absolute distance scale for: Type Ia and II SNe Tully-Fisher Relation Fundamental Plane for Ellipticals Surface Brightness Fluctuations
Cosmic Distance Scale
Cepheid Variables Lie on instability strip of HR diagram Instability leads to pulsations and variability Strong correlation between period of pulsation and luminosty of Cepheid
Cepheid Variables Lie on instability strip of HR diagram Instability leads to pulsations and variability Strong correlation between period of pulsation and luminosty of Cepheid
Cepheid Variables Lie on instability strip of HR diagram Instability leads to pulsations and variability Strong correlation between period of pulsation and luminosty of Cepheid
Advantages of Cepheids Among brightest stellar indicators Abundant in spiral galaxies Long lifetimes Small scatter in PL relation Studied and modeled extensively
Disadvantages of Cepheids Young stars, founds in dusty regions Dependence of PL relation on metallicity Resolving individual Cepheids becomes difficult at greater distances Limited to < 30 Mpc
Searching for Cepheids Search target spiral galaxies in regions of active star-formation, but low in dustextinction Observe with WFPC2 in V and I bands to correct for dust Targeted 31 galaxies to find distance, calibrate secondary methods, and test effects of metallicity on PL relation
Measuring Cepheid Distances Large Magellanic Cloud PL relation used as a fiducial Distance modulus: 0 = 18.50 mag Distance of 50 kpc Mean reddening E (V-I) = 0.13 i- 0 = 5 log(d i /d 0 )
Effect of Metallicity Longstanding uncertainty in Cepheid distance Calibrating metallicity effects from theoretical models was still unfeasible Empirical values from Cepheids in M31 and M101 suggest 0< VI <-0.4 Adopted VI = -0.2 ±0.2 mag/dex
Adopting PL Relations Udalski et al. (1999) studied more LMC Cepheids, improved calibration With improved Udalski data, adopted period-luminosity relations become: And the true distance modulus for galaxies: where
Effects of Udalski PL Slopes V-band PL Slope remained -2.76 I-band PL Slope changed from -3.06 to -2.96 New Calibration predicts higher reddening therefore, smaller distances Systematically higher reddening for longer period Cepheids difference is largest at greater distances
Local Flow Field H 0 requires knowing distance and velocity Peculiar velocities of nearby galaxies complicate measuring Hubble velocity => H 0 measurements more accurate at higher distances
Cepheid Hubble Diagram 23 galaxies with Cepheid distances Slope of 75 km s -1 Mpc -1, excluding systematic errors Scatter is larger than in secondary methods (local flow), but in good agreement
Secondary Distance Methods
Cumulative H0 Values
Cumulative Hubble Diagram
Overall Systematic Error Uncertainty in the zero point of PL relation Effect of reddening and metallicity on observed PL relations Effects of incompleteness bias and crowding on Cepheid distances Velocity perturbation about the Hubble flow Overall Systematic uncertainty: ±10%
Implications for Cosmology Knowing H 0, the average density of matter, and, the Friedmann equation yields a measure of the expansion age of Universe For, H 0 = 72 km s -1 Mpc -1, m =0.3, =0.7, the expansion age is 13 ±1 Gyr Consistent with globular cluster ages
References Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant Freedman, Madore, Gibson, et al., Astrophysical Journal 553, pp. 47. Images from: hubblesite.org/gallery/spacecraft/03/ http://ircamera.as.arizona.edu/natsci102/images/distladder.jpg http://odin.physastro.mnsu.edu/~eskridge/astr101/kauf21_12.jpg http://will114.asu.edu/varstar.pdf http://www.astronomy.com/asy/objects/images/cepheid_p-l_600. jpg http://seds.lpl.arizona.edu/messier/pics/more/m81cep_hs.jpg http://heritage.stsci.edu/2006/07/images/i0607aw.jpg
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